CN111250546A - Edge thinning multipoint optimization control method based on interior point penalty function method - Google Patents

Edge thinning multipoint optimization control method based on interior point penalty function method Download PDF

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CN111250546A
CN111250546A CN202010018520.0A CN202010018520A CN111250546A CN 111250546 A CN111250546 A CN 111250546A CN 202010018520 A CN202010018520 A CN 202010018520A CN 111250546 A CN111250546 A CN 111250546A
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edge
thinning
interior point
penalty function
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CN111250546B (en
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王鹏飞
段树威
李旭
王东城
杨利坡
刘宏民
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Yanshan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B21B37/40—Control of flatness or profile during rolling of strip, sheets or plates using axial shifting of the rolls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B38/00—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product
    • B21B38/04—Methods or devices for measuring, detecting or monitoring specially adapted for metal-rolling mills, e.g. position detection, inspection of the product for measuring thickness, width, diameter or other transverse dimensions of the product

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Abstract

The invention discloses an edge thinning multipoint optimization control method based on an interior point penalty function method, which belongs to the technical field of metallurgical rolling and comprises the following steps: the method comprises the following steps: collecting data from the edge thinning detection device in real time and processing the data; step two, calculating the influence degree of the thinning of the transverse moving edge of the working roll by a finite element simulation method, and establishing a regulation and control efficiency coefficient matrix; calculating the adjustment amount of the adjustment mechanism based on an interior point penalty function method; and step four, outputting the transverse moving amount to a working roller transverse moving executing mechanism. According to the edge thinning multipoint control method, the regulation and control efficiency coefficient vector is established through finite element simulation, the multi-target monitoring and optimization are carried out on the edge of the strip steel by adopting an optimization method of an inner point penalty function, the multi-target optimization of edge thinning is realized, the continuity of the edge thinning of the strip steel is comprehensively considered, and the control precision of the edge thinning is improved.

Description

Edge thinning multipoint optimization control method based on interior point penalty function method
Technical Field
The invention relates to the technical field of metallurgical rolling, in particular to edge thinning control of cold-rolled silicon steel.
Background
Cold rolled silicon steel is a special steel plate which is an important soft magnetic alloy in the electric power industry, the electronic industry and the military industry and can effectively convert electromagnetism. Cold rolled silicon steel is commonly used in the manufacture of motors or transformers and requires lamination of strips with edge thinning defects, which have a slight individual crown difference and the cumulative thickness after lamination may become unacceptably large. The magnetic conductivity is not uniform, so that the steel for electrical engineering is mainly used for manufacturing transformers and motors, and the control difficulty of edge thinning is relatively high due to the fact that the silicon content in silicon steel is high.
Many scholars have analyzed the generation mechanism, influencing factors and prediction models around edge thinning by building mathematical analysis models and finite element simulation models. These methods theoretically analyze the thinning of the edge portions in detail, but no feasible control method is proposed. Later, along with the increase of control equipment and detection equipment for edge thinning, japanese hitachi proposed a single-point control method and put into production to achieve certain effects, but along with the continuous improvement of control accuracy, domestic colleges and universities including beijing university of science and technology proposed a three-point control method to improve the control accuracy of edge thinning. Considering that the thickness distribution of the strip steel is continuous and should not be limited to three-point control, the control method in the prior art is not ideal.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an edge part thinning multipoint optimization control method based on an interior point penalty function method, so that edge part thinning multi-target optimization is realized, the continuity of strip steel edge part thinning is comprehensively considered, and the control precision of edge part thinning is improved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
an edge thinning multipoint optimization control method based on an interior point penalty function method comprises the following steps:
step one, acquiring data in real time from an edge thinning detection device and carrying out filtering processing;
step two, calculating the influence degree of the thinning of the transverse moving edge of the working roll by a finite element simulation method, and establishing a regulation and control efficiency coefficient matrix;
calculating the adjustment amount of the adjustment mechanism based on an interior point penalty function method;
and step four, outputting the transverse moving amount to a working roller transverse moving executing mechanism.
The technical scheme of the invention is further improved as follows: in the first step, a side descending instrument is configured at an outlet of a fifth rack, the side descending instrument is used for detecting and constantly transmitting the transverse thickness deviation of the edge area of the finished strip steel product, the side descending instrument has 42 detection sections, and the side descending instrument comprises 3 measuring heads, two edge measuring heads and 1 central line measuring head from 1C-shaped rack; each edge head contains 15 detectors and the central head contains 12 detectors; the edge drop instrument can realize automatic edge finding, after an actual measurement signal is obtained, whether the detection data of the edge drop instrument is normal or not is judged, namely whether the detection data is changed or not is judged, then filtering processing is carried out to detect whether the edge drop values of a transmission side and a transmission side exceed a dead zone or not, and if the edge drop values do not exceed a dead zone limit value, edge drop control is not carried out;
the filter formula is as follows:
hi＝hi+(1-β)·(hi-hi-1)
in the formula hiThe ith detection value is β is a filter factor, the value range of β is (0, 1), hi-1The detection value is the detection value of the (i-1) th time.
The technical scheme of the invention is further improved as follows: the second specific process comprises the following steps:
establishing a corresponding finite element simulation model or calculating the influence of the shifting of the working roll on the edge thinning by setting different transverse displacement amounts in a mathematical analysis mode, and performing derivation processing on the influence to obtain a working roll shifting regulation and control efficiency coefficient vector;
the working roll shifting regulation and control efficiency coefficient vector is as follows:
effw1＝[effw1,1,effw1,2,……,effw1,n]
effw2＝[effw2,1,effw2,2,……,effw2,n]
effw3＝[effw3,1,effw3,2,……,effw3,n]
in the formula of effw1，effw1，effw1The roll shifting regulation and control efficacy vectors, eff, corresponding to the first, second and third working rolls respectivelyw1，nIs the coefficient, eff, of the regulation efficacy coefficient vector of the 1 st frame corresponding to n pointsw2，nIs the coefficient, eff, of the regulatory efficacy coefficient vector of n points corresponding to the 2 nd framew3，nIs the coefficient of the regulation efficacy coefficient vector of the 3 rd frame corresponding to n points.
The technical scheme of the invention is further improved as follows: the concrete process of the third step is as follows:
the transverse displacement of the working rollers is actually limited, the value calculated by the optimization method is an executable value by restricting the maximum transverse displacement and the minimum transverse displacement of each working roller, and the interior point penalty function method converts the restriction problem into an unconstrained problem;
objective function
Figure BDA0002359839000000031
Wherein x1, x2 and x3 are respectively the adjustment quantity of the working roll corresponding to the first, the second and the third machine frames, and ED edge drop target vector
Constraint function
g1(x)＝-x1<0
g2(x)＝-x2<0
g3(x)＝-x3<0
g4(x)＝x1-limitW1<0
g5(x)＝x2-limitw2<0
g6(x)＝x3-limitw3<0
Limit in the formulaW1Is the maximum value of the adjustment amount of the first frame work roll; limitW2Is the maximum value of the adjustment quantity of the working roll of the second frame; limitW3Is the maximum value of the adjustment quantity of the working roll of the third frame;
selecting an interior point punishment method, wherein the punishment function is in the form of
Figure BDA0002359839000000033
r(k-1)·c＝r(k)
In the formula, r(k)And the penalty factor of the k time is reduced by a factor c.
The technical scheme of the invention is further improved as follows: the fourth step is specifically as follows: and (4) calculating the transverse displacement of each working roller through an optimal algorithm in the three steps, outputting the transverse displacement to an executing mechanism, and then calculating in the next detection period.
Due to the adoption of the technical scheme, the invention has the technical progress that:
according to the edge thinning multipoint control method, the regulation and control efficiency coefficient vector is established through finite element simulation, the multi-target monitoring and optimization are carried out on the edge of the strip steel by adopting an optimization method of an inner point penalty function, the multi-target optimization of edge thinning is realized, the continuity of the edge thinning of the strip steel is comprehensively considered, and the control precision of the edge thinning is improved.
Drawings
FIG. 1 is a flow chart of a control method of the present invention;
FIG. 2 is a process of a Powell optimization algorithm;
fig. 3 is a flow chart of an edge drop closed loop control system.
Detailed Description
The present invention will be described in further detail with reference to the following examples:
the embodiment discloses operation steps of an adjusting method of a target curve of a cold-rolled online plate shape of a 1450mm five-stand cold continuous rolling unit. The plate shape adjusting mechanism comprises a roll inclination, a working roll positive/negative bending roll, a middle roll positive bending roll and middle roll transverse moving and a working roll transverse moving, and main control parameters and rolling parameters are shown in the following table.
TABLE 1 Main parameters of the Rolling Process
Figure BDA0002359839000000041
Figure BDA0002359839000000051
As shown in fig. 1, the multi-point control method for edge thinning based on the interior point penalty function method includes the following steps:
the method comprises the following steps: real-time data acquisition and filtering processing from edge thinning detection device
In production, an outlet of the fifth rack is provided with a side descending instrument which is mainly used for detecting the transverse thickness deviation of the edge area of the finished strip steel product, and the side descending instrument transmits thickness detection data in real time, namely the transverse thickness deviation of the edge area. The limit falls the appearance and has 42 detection sections altogether, and basically, the limit falls the appearance and contains 3 measuring heads, two limit measuring heads and 1 central line measuring head by 1C type frame. Each edge head contains 15 detectors and the central head 12 detectors. The edge drop instrument can realize automatic edge finding, after an actual measurement signal is obtained, whether the detection data of the edge drop instrument is normal or not is judged, namely whether the detection data are changed or not is judged, then filtering processing is carried out to detect whether the edge drop values of the transmission side and the transmission side exceed a dead zone or not, and if the edge drop values do not exceed a dead zone limit value, edge drop control is not carried out.
The filter formula is as follows:
hi＝hi+(1-β)·(hi-hi-1)
this filtering factor β is 0.2.
In the formula hiThe ith detection value is β is a filter factor, the value range of β is (0, 1), hi-1The detection value is the detection value of the (i-1) th time.
And step two, calculating the influence degree of the thinning of the transverse moving edge of the working roll by a finite element simulation method, and establishing a regulation and control efficiency coefficient matrix.
And establishing a corresponding finite element simulation model according to the actual process and production conditions on site or calculating the influence of the roll shifting of the working roll on the edge thinning by setting different transverse displacement in a mathematical analysis mode, and carrying out derivation treatment on the influence to obtain the regulation and control efficiency coefficient vector of the roll shifting of the working roll.
The working roll shifting regulation and control efficiency coefficient vector is as follows:
effw1＝[effw1,1,effw1,2,……,effw1,n]
effw2＝[effw2,1,effw2,2,……,effw2,n]
effw3＝[effw3,1,effw3,2,……,effw3,n]
in the formula of effw1，effw1，effw1The roll shifting regulation and control efficacy vectors, eff, corresponding to the first, second and third working rolls respectivelyw1，nIs the coefficient, eff, of the regulation efficacy coefficient vector of the 1 st frame corresponding to n pointsw2，nIs the coefficient, eff, of the regulatory efficacy coefficient vector of n points corresponding to the 2 nd framew3，nIs the coefficient of the regulation efficacy coefficient vector of the 3 rd frame corresponding to n points.
Step three, calculating the adjustment quantity of the adjustment mechanism based on an interior point penalty function method
The internal penalty function method, also called obstacle penalty function method, is a method that searches inside a feasible region, the constraint boundary acts like a fence, the penalty function value is very small if the current solution is far from the constraint boundary, otherwise it is close to infinity. The interior point penalty function method is a constrained optimization method, because of the practical engineering problem, the transverse displacement of the working rollers is practically limited, and the value calculated by the optimization method is an executable value by constraining the maximum transverse displacement and the minimum transverse displacement of each working roller.
The interior point penalty function method converts the constraint problem into an unconstrained problem, and the unconstrained problem is based on a Powll optimization function method.
Objective function
Figure BDA0002359839000000061
Wherein x1, x2 and x3 are respectively the adjustment quantities corresponding to the first rack, the second rack and the third rack, and the ED edge drop target vector;
constraint function
g1(x)＝-x1<0
g2(x)＝-x2<0
g3(x)＝-x3<0
g4(x)＝x1-limitW1<0
g5(x)＝x2-limitw2<0
g6(x)＝x3-limitw3<0
Limitw1＝110，Limitw1＝90，Limitw1＝70。
Selecting an interior point punishment method, wherein the punishment function is in the form of
Figure BDA0002359839000000071
r(k-1)·c＝r(k)
Get x(0)＝[1,1,1]T,r(0)3, c is 0.7, and the calculation accuracy epsilon is 0.01
In the formula x(0)To search for an initial point, r(0)For the penalty factor, the factor c is reduced.
The unconstrained problem in the invention is based on a Powell optimization function method, and the Powell optimization method is a solution method based on a conjugate direction.
As shown in fig. 2, an initial point X0(1) is selected, and an initial direction S1(1) ═ e1 ═ 1, 0'; s2(1) ═ e2 ═ 0, 1';
a first round of circulation:
initial point X0(1)---->(e1,e2)---->End point X2(1)---->Generating a new direction S(1)＝X2(1)-X0(1)；
And (3) second round circulation:
initial point X0(2)---->(e2,S(1))---->End point X2(2)---->Generating a new direction S(2)＝X2(2)-X0(2)；
We will find, from the above figure, that point X0(2)、X2(2)Is sequentially arranged along the S twice(1)And direction one-dimensional search is carried out to obtain a minimum point. From the conjugation one can obtain: connection X0(2)And X2(2)Formed vector S(2)And S(1)Conjugation to H.
Theoretically, the two-dimensional quadratic positive definite function iterates points through one-dimensional search of the set of conjugate directions to reach a minimum point X of the function.
Generalizing this structure to an n-dimensional quadratic positive definite function, i.e. sequentially along n (S)(1)，S(2)，...，S(n)) The conjugate direction one-dimensional search can reach the limit value point.
Step four, outputting the transverse displacement to a transverse displacement executing mechanism of the working roller
And calculating the transverse displacement of each working roller through an optimal algorithm in the three steps, and outputting the transverse displacement to an actuator, wherein the transverse displacement of the working rollers is determined by the values of x1, x2 and x3, and then calculating in the next detection period.

Claims (5)

1. An edge thinning multipoint optimization control method based on an interior point penalty function method is characterized by comprising the following steps:
step one, acquiring data in real time from an edge thinning detection device and carrying out filtering processing;
step two, calculating the influence degree of the thinning of the transverse moving edge of the working roll by a finite element simulation method, and establishing a regulation and control efficiency coefficient matrix;
calculating the adjustment amount of the adjustment mechanism based on an interior point penalty function method;
and step four, outputting the transverse moving amount to a working roller transverse moving executing mechanism.
2. The edge thinning multipoint optimization control method based on the interior point penalty function method according to claim 1, characterized in that: in the first step, a side descending instrument is configured at an outlet of a fifth rack, the side descending instrument is used for detecting and constantly transmitting the transverse thickness deviation of the edge area of the finished strip steel product, the side descending instrument has 42 detection sections, and the side descending instrument comprises 3 measuring heads, two edge measuring heads and 1 central line measuring head from 1C-shaped rack; each edge head contains 15 detectors and the central head contains 12 detectors; the edge drop instrument can realize automatic edge finding, after an actual measurement signal is obtained, whether the detection data of the edge drop instrument is normal or not is judged, namely whether the detection data is changed or not is judged, then filtering processing is carried out to detect whether the edge drop values of a transmission side and a transmission side exceed a dead zone or not, and if the edge drop values do not exceed a dead zone limit value, edge drop control is not carried out;
the filter formula is as follows:
hi＝hi+(1-β)·(hi-hi-1)
in the formula hiThe ith detection value is β is a filter factor, the value range of β is (0, 1), hi-1The detection value is the detection value of the (i-1) th time.
3. The edge thinning multipoint optimization control method based on the interior point penalty function method according to claim 2, characterized in that the second specific process is as follows:
establishing a corresponding finite element simulation model or calculating the influence of the shifting of the working roll on the edge thinning by setting different transverse displacement amounts in a mathematical analysis mode, and performing derivation processing on the influence to obtain a working roll shifting regulation and control efficiency coefficient vector;
the working roll shifting regulation and control efficiency coefficient vector is as follows:
effw1＝[effw1,1,effw1,2,……,effw1,n]
effw2＝[effw2,1,effw2,2,……,effw2,n]
effw3＝[effw3,1,effw3,2,……,effw3,n]
in the formula of effw1，effw1，effw1The roll shifting regulation and control efficacy vectors, eff, corresponding to the first, second and third working rolls respectivelyw1，nIs the coefficient, eff, of the regulation efficacy coefficient vector of the 1 st frame corresponding to n pointsw2，nIs the coefficient, eff, of the regulatory efficacy coefficient vector of n points corresponding to the 2 nd framew3，nIs the coefficient of the regulation efficacy coefficient vector of the 3 rd frame corresponding to n points.
4. The edge thinning multipoint optimization control method based on the interior point penalty function method according to claim 3, characterized in that the specific process of the third step is as follows:
the transverse displacement of the working rollers is actually limited, the value calculated by the optimization method is an executable value by restricting the maximum transverse displacement and the minimum transverse displacement of each working roller, and the interior point penalty function method converts the restriction problem into an unconstrained problem;
objective function
Figure FDA0002359838990000021
Wherein x1, x2 and x3 are respectively the adjustment quantity of the working roll corresponding to the first, the second and the third machine frames, and the delta ED edge drop target vector
Constraint function
g1(x)＝-x1<0
g2(x)＝-x2<0
g3(x)＝-x3<0
g4(x)＝x1-limitW1<0
g5(x)＝x2-limitw2<0
g6(x)＝x3-limitw3<0
Limit in the formulaW1Is the maximum value of the adjustment amount of the first frame work roll; limitW2Is the maximum value of the adjustment quantity of the working roll of the second frame; limitW3Is the maximum value of the adjustment quantity of the working roll of the third frame;
selecting an interior point punishment method, wherein the punishment function is in the form of
Figure FDA0002359838990000031
r(k-1)·c＝r(k)
In the formula, r(k)And the penalty factor of the k time is reduced by a factor c.
5. The edge thinning multipoint optimization control method based on the interior point penalty function method according to claim 4, characterized in that the fourth step is specifically: and (4) calculating the transverse displacement of each working roller through an optimal algorithm in the three steps, outputting the transverse displacement to an executing mechanism, and then calculating in the next detection period.
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CN112836348A (en) * 2021-01-08 2021-05-25 燕山大学 Strip-shaped mechanism regulating quantity optimization method based on genetic algorithm and penalty function method
CN114798727A (en) * 2022-04-14 2022-07-29 北京科技大学 Multi-objective optimization-based specification self-adaptive rolling method and device and electronic equipment

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CN112836348A (en) * 2021-01-08 2021-05-25 燕山大学 Strip-shaped mechanism regulating quantity optimization method based on genetic algorithm and penalty function method
CN114798727A (en) * 2022-04-14 2022-07-29 北京科技大学 Multi-objective optimization-based specification self-adaptive rolling method and device and electronic equipment
CN114798727B (en) * 2022-04-14 2022-11-11 北京科技大学 Multi-objective optimization-based specification self-adaptive rolling method and device and electronic equipment

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